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## Introduction

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0001
- Subject:
- Mathematics, Geometry / Topology

This chapter explains that the book deals with quotients of the complex 2-ball yielding finite coverings of the projective plane branched along certain line arrangements. It gives a complete list of ... More

## Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

*Paula Tretkoff*

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More

## Appell Hypergeometric Functions

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0008
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the complete quadrilateral line arrangement, and especially its relationship with the space of regular points of the system of partial differential equations defining the ... More

## Line Arrangements in P2(C) and Their Finite Covers

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0006
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the free 2-ball quotients arising as finite covers of the projective plane branched along line arrangements. It first considers a surface X obtained by blowing up the singular ... More

## Complex Surfaces and Coverings

*Paula Tretkoff*

### in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691144771
- eISBN:
- 9781400881253
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691144771.003.0004
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with complex surfaces and their finite coverings branched along divisors, that is, subvarieties of codimension 1. In particular, it considers coverings branched over transversally ... More

## Block designs

*NORMAN BIGGS and ROBIN WILSON*

### in Combinatorics: Ancient and Modern

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.003.0011
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

This chapter outlines the origins of design theory, with particular reference to the ‘Steiner triple systems’, the pioneering work of Thomas Kirkman, and early contributions by a number of writers on ... More

## Spectral Sequences

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0006
- Subject:
- Mathematics, Educational Mathematics

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined ... More

## Cohomology of Homotopy 2-types

*Graham Ellis*

### in An Invitation to Computational Homotopy

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198832973
- eISBN:
- 9780191871375
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198832973.003.0005
- Subject:
- Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using ... More

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